By using moving frame theory,first we introduce 2p-th mean curvatures and(2p+1)-th mean curvature vector fields for a submanifold.We then give an integral expression of them that characterizes them as mean values of s...By using moving frame theory,first we introduce 2p-th mean curvatures and(2p+1)-th mean curvature vector fields for a submanifold.We then give an integral expression of them that characterizes them as mean values of symmetric functions of principle curvatures.Next we apply it to derive directly the celebrated Weyl-Gray tube formula in terms of integrals of the 2p-th mean curvatures and some Minkowski-type integral formulas.展开更多
基金the National Natural Science Foundation of China(Grant No.107010007)
文摘By using moving frame theory,first we introduce 2p-th mean curvatures and(2p+1)-th mean curvature vector fields for a submanifold.We then give an integral expression of them that characterizes them as mean values of symmetric functions of principle curvatures.Next we apply it to derive directly the celebrated Weyl-Gray tube formula in terms of integrals of the 2p-th mean curvatures and some Minkowski-type integral formulas.
